The Robust Performance Of Near Field Beamforming In Worst-case Environment

With the increasing development of array signal processing, its status in modern signalprocessing has become significant and has been applied in many fields, such as radar,communications, radio astronomy and medical diagnosis. Adaptive beamforming is animportant part of array signal processing; its target is to obtain the optimal output by assigningdifferent factor to every array element. Most conventional adaptive algorithms are obtained inideal environment, but this condition can not be satisfied in practical applications and maylead to a decline of output performance. So, it is necessary to analysis the robustness of thebeamforming algorithm. Therefore most existing algorithms assume that the source locates infar field of the array and the signal has a plane wave front. However, in in-vehicle systemsand telephone conference, the assumption is not established. So, study near fieldbeamforming algorithm and its robustness is particularly important for practical applications.In this paper, the robust performance of near field in worst-case environment has beendiscussed deeply.Firstly, we derive the expression of near field spherical wave array response. Theresponse is related to not only the orientation but also the distance between the source and thesensor array. This makes the problem more complex than receive or extract far field signals.Secondly, a uniform circular array is used to study the output performance of SMI and LSMIalgorithm in near field. Simulation results with different sample number and the input SNRshow that both algorithms can be applied to near field beamforming. And the LSMI algorithmhas better robustness. It can effectively avoid disturbance of the optimal vector caused by theeigenvectors that corresponded to the small eigenvalues. Once more, we focus on near fieldbeamforming algorithm in worst-case environment and derive the formation process withsome guidelines in detail. By introducing the ellipsoid set of constraints, we achieve thedistortion free reception of the signal with arbitrary direction vector mismatch. The algorithmcan be transformed into a convex optimization problem under certain conditions and theoptimal weight can be obtained by interior point method. Finally the algorithm is applied toboth a single signal and multi-signal receiving in near field. Simulation results verify that thealgorithm has better robustness according to the situation with direction vector mismatch orsmall sample number or high input SNR. Simulation results verify the validity and applicability of the algorithm.